An angle measure of 630 degrees was written in radians as $x\pi$. What is the value of $x$?

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A circle is $360\degree$ or $2\pi$ radians. We use can a simple proportion to find the correct number of radians.

$$\frac{2\pi \text{ radians}}{360\degree} = \frac{R \text{ radians}}{630\degree}$$ $$2\pi \cdot 630 = 360 \cdot R$$ $$1260=360R$$ $$\frac{1260\pi}{360}=R$$ $$3.5\pi=R$$ $$R= \boxed{\frac{7}{2}}\pi$$

We can do unit conversions as long as we know the conversion, $\pi\text{ radians}=180\degree$.

$$630 \degree \cdot \frac{\pi \text{ radians}}{180 \degree}$$ $$630\cdot \frac{\pi}{180} \text{ radians}$$ $$=\frac{63}{18}\pi$$ $$= \frac{21}{6}\pi$$ $$= \boxed{\frac{7}{2}}\pi$$